Experimental study of the Fermi–Pasta–Ulam recurrence in a bi-modal electrical transmission line

Farota, Abdou Karim; Faye, Mansour M

doi:10.1088/0031-8949/88/05/055802

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…In fact, the NLSE model predicts a fully reversible or spatially periodic power exchange among the pump, the initial modulation sidebands and all their harmonics. This process can be described in terms of exact solutions of the NLSE [9][10][11][12], and it has been experimentally observed in deep water waves [13,14], nonlinear optical fibers [15][16][17][18][19][20], nematic liquid crystals [21], magnetic film strip-based active feedback rings [22], and bimodal electrical transmission lines [23]. Useful physical insight into the qualitative dynamics of FPU recurrence, such as for example the presence of separatrix solutions, or the dependence of the FPU recurrence period upon the input relative phase between the pump and the initial modulation sidebands, may be obtained by using a three-wave truncation which leads to a fully integrable, one-dimensional equivalent particle model [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

Wabnitz

Wetzel

2014

Physics Letters A

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We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.

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Section: Introductionmentioning

confidence: 99%

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

Wabnitz

Wetzel

2014

Physics Letters A

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“…We also studied the evolution of the return period depending on the amplitude of the signal in the BF mode and frequency f = 475 KHz. By varying the amplitude of the input signal offered in the line, we see a linear dependence of the period of recurrence with the inverse of the square root of the amplitude of the voltage of the signal [19] (Figure 20). Toda [20], in the case of the electric transmission line mono-modal,determined theoretically this dependence of the return period with the amplitude of the applied signal.…”

Section: Evolution Of the Period Of Recurrence Based On The Amplitudementioning

confidence: 99%

“…resorted the spectral analysis of the transform of Fourier to ensure that the wave has covered its sinusoidal shape. In precedent works [18,19], we present the evolution of the signal and Fourier transformation (signal frequency f = 910 kHz, Vsignal = 2.2 V and polarized voltage V 0 = 1.5 V). In these works, we see that the amplitude of the signal of the positive half-wave is higher than that of the wave for the negative alternation.…”

Section: The Fpu Recurrence In the Hf Modementioning

confidence: 99%

Experimental Studies of the Electrical Nonlinear Bimodal Transmission Line

Farota¹,

Faye²,

Diop³

et al. 2018

Advanced Electronic Circuits - Principles, Architectures and Applications on Emerging Technologies

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After a few years of calm, the investigations on the dynamic, especially nonlinear, systems returned to the front of the research in non-linear physics. We propose, in this chapter, a study of an electrical nonlinear transmission line, realized in a previous work, to use the latter to highlight certain properties (modulation instability-MI, Fermi-Pasta-Ulam (FPU) recurrence, fragmentation of solitons in wave trains, multiplication(increase) and division of frequencies, etc.), which are observed in several domains in applied physics: hydraulic, artificial neuronal, network physical appearance (physics) of the plasma, and the circulation.

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“…1 and recovered results that corroborated the theoretical previsions. [28] Moreover, Farota et al investigated experimentally the entire properties of the electrical NLBTL. [29]…”

Section: Structural Dynamics Of the Networkmentioning

confidence: 99%

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

Ngounou¹,

Pelap²

2021

Chinese Phys. B

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This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg–Landau equation instead of a Korteweg–de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.

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Experimental study of the Fermi–Pasta–Ulam recurrence in a bi-modal electrical transmission line

Cited by 4 publications

References 10 publications

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

Experimental Studies of the Electrical Nonlinear Bimodal Transmission Line

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

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